Although a radio frequency signal power amplifier is crucial to a radio frequency communication transmitter, its non-linear characteristics cause distortion to radio frequency signals. In view of this, it is important to optimize its non-linear characteristics. Referring to FIG. 1, an adaptive digital pre-distortion (DPD) framework comprises a modulator (MOD) 110, a pre-distorter 120, a transmitting circuit 130, a receiving circuit 140, and an extraction module 150. The prior art discloses that the pre-distorter 120 operates in conjunction with a monitoring receiver, so as for the extraction module 150 to perform signal model parameter extraction by signal waveform distortion standards, and then the pre-distorter 120 adjusts its input/output response relationship in accordance with the extracted parameter, thereby correcting the distortion.
A typical memory polynomial model and its related parameter extraction equation are shown below.
                                                                                          r                  ^                                B                            ⁡                              [                n                ]                                      =                                          DPD                ⁢                                  {                                                            r                      →                                        B                                    }                                            =                                                                                          ∑                                              q                        =                        0                                            Q                                        ⁢                                                                  ∑                                                  l                          =                          1                                                L                                            ⁢                                                                        a                                                      q                            ,                            l                                                                          ·                                                                              r                            B                                                    ⁡                                                      [                                                          n                              -                              q                                                        ]                                                                          ·                                                                                                                                                                        r                                B                                                            ⁡                                                              [                                                                  n                                  -                                  q                                                                ]                                                                                                                                                                      l                            -                            1                                                                                                                                ≈                                                                                    s                        ^                                            B                                        ⁡                                          [                      n                      ]                                                                      ⇒                                                      min                                          A                      →                                                        ⁢                                                                                                                                    R                          ·                                                      A                            →                                                                          -                                                                                                            s                              ^                                                        →                                                    B                                                                                                            2                                                                                ⁢                                          ⁢                                          ⁢                                    A              →                        =                          [                                                                                          a                                              q                        ,                        l                                                              |                    q                                    =                                      0                    ∼                    Q                                                  ,                                  l                  =                                      1                    ∼                    L                                                              ]                                      ⁢                                  ⁢                                  ⁢                  R          =                                                    [                                                                                                                                                          r                            B                                                    ⁡                                                      [                                                          n                              -                              q                                                        ]                                                                          ·                                                                                                                                                                        r                                B                                                            ⁡                                                              [                                                                  n                                  -                                  q                                                                ]                                                                                                                                                                      l                            -                            1                                                                                              |                      q                                        =                                          0                      ∼                      Q                                                        ,                                      l                    =                                          1                      ∼                      L                                                        ,                                                                          ⁢                                                                          ⁢                                      n                    =                                          0                      ∼                                              N                        -                        1                                                                                            ]                            ⁢                                                          ⁢                                                          ∴                                                A                  →                                                  SD                  ,                  opt                                                      =                                                            (                                                            R                      H                                        ·                    R                                    )                                                  -                  1                                            ·                              R                H                            ·                                                                    s                    ^                                    →                                B                                                                        (        1        )            
As indicated by equation (1), not only does parameter extraction require intricate matrix-based computation, but linear channel distortion in the transmitting module is also included in the digital pre-distortion framework. As a result, even if the non-linear amplifier approximates to a memoryless non-linear model, the memory polynomial model is not going to disappear, and thus overall structural complexity remains unabated.
Furthermore, conventional pre-distortion technology usually involves optimizing the polynomial coefficients by the full-range input/output relationship of a digital pre-distorter, but doing so inevitably increases the complexity of a pre-distortion system, consumes much computation resources, and renders pre-distortion processing inefficient. Accordingly, pre-distortion technology still has room for improvement in terms of the reduction in the complexity of pre-distortion processing.